In urban areas, I’m used to house numbers starting at 1 at one end of the street, then incrementing as you go along.

Yes, this is a thing, but not always.

In my own subdivision all the residential streets start with the same letter, and the housing numbers are in the hundreds (300, 400, 500, etc.), even though the streets are short. None of them start at 1, or even 10, or even 100! ... there's no rhyme or reason, but it does cause confusion when you have several "630" house numbers all in the same area but on different streets that are slightly different.

why would the house numbers be different?

To make up for the similar street names, of course. The start number of a series of street addresses is a totally arbitrary choice afaik, especially when there's a chance the street might grow in either direction in the future.

In my area, we have a grid pattern, so there is one intersection that is the 0/0 mark, and addresses all start from there. Each block is 100 addresses, so the first block North would be 0-99 North Main St, the next would be 100-199 North Main St, and so on. Some numbers are skipped, because I think the address can even be used to know the number of feet from the corner the property starts at.

Now, if a street starts 6 blocks south of the 0 line, it's addresses start at 600 South Something Road. It takes some getting used to, but once you learn it, it's really useful to be able to get to a new place without directions.

My work calls for me to log addresses and map them out a ton. I can tell you from experience that there can be an 1191 11th Ct, 1191, 11th Ave, and 1191 11th Dr all within one block. It's infuriating enough for me just mixing them up, I can't imagine driving around not realizing that the other two even exist would make it way more confusing.